A study of double- and multi-mode RR Lyrae variables

We present the results of our new study of known RR Lyrae variable stars. All observations available for these stars in the Catalina Surveys were analyzed, and double-mode variations were identified. We studied the Petersen diagram and period distribution for the double-mode RR Lyrae variables in the Galactic field, pulsating in the first-overtone and fundamental modes. The double-peaked character of the period distribution was detected for Galactic RR(B) stars, corresponding to Oosterhoff's classes of globular clusters, which indicates that the age and evolution stage of RR(B) stars in the field and RR Lyrae variables in globular clusters are probably the same. Besides, we discovered five RRC stars with two simultaneously excited non-radial pulsations (equidistant triplets).Comment: 10 pages, 5 figures, 2 table

Nonlinear dynamics of solitons for the vector modified Korteweg-de Vries equation

We consider the vector generalization of the modified Korteweg-de Vries equation. We develop the inverse scattering transform for solving this equation. We construct the solitons and the breather solutions and investigate the processes of their collisions. We show that along with one-component soliton solutions, there are solutions which have essentially three-component structure

Homogenization of attractors of non-linear evolutionary equations

The paper is devoted to the homogenization of non{linear evolutionary equations in domains with "traps"

Global weak solutions of the Navier--Stokes--Vlasov--Poisson system

We consider the Navier-Stokes-Vlasov-Poisson system of partial differential equations, describing the motion of a viscous incompressible fluid with small solid charged particles therein. We prove the existence of a weak global solution of the initial boundary value problem for this system